With these decompositions in hand, we now proceed by constructing possible CB stratifications. Let us begin by assuming flavor symmetry \(\mathfrak {su}(5)\)  and scaling dimensions \(\left(\Delta _{u_1}, \Delta _{u_2} \right) = \left({4\over 3} ,{8\over 3} \right)\) . From Proposition REF , we know that the full flavor symmetry must be realized on at least one codimension-one stratum, which according to Table REF  can only be a \([I_5, \mathfrak {su}(5)]\)  stratum. We may still allow for unflavored strata \({\cal T}_{\varnothing , 1}^{(1)}\)  and \([I_1, \varnothing ]\) .The careful reader might notice that \([I_1, \varnothing ]\)  has a \(U(1)\)  flavor symmetry, and thus might object to use of the word “unflavored.” However, here we are only interested in flavor factors which act on the CB by “splitting” the singular locus. Because the \(U(1)\)  mass deformation does not split the \(I_1\)  singularity (see e.g. [1]}) the \([I_1, \varnothing ]\)  stratum is effectively unflavored. This is to be contrasted with the cases of \({\cal S}_{\varnothing ,3}^{(1)}\)  and \({\cal S}_{\varnothing ,4}^{(1)}\) , which also have \(U(1)\)  flavor symmetry, but for which the \(U(1)\)  splits the singular locus. From Proposition REF , we know that unknotted strata can only be of the form \(u_2=0\) , since \(\Delta _{u_2} = {8 \over 3}\)  is not on the list of allowed rank-one Coulomb branch dimensions. Thus both knotted and unknotted strata must have \(\Delta ^{\mathrm {sing}}_i = {8\over 3}\) .
